Discrete Ricci Curvature on Complex Network Topologies: An Application to Management Information System Networks
MATHEMATICS, cilt.14, sa.15, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 15
- Basım Tarihi: 2026
- Doi Numarası: 10.3390/math14152760
- Dergi Adı: MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Hatay Mustafa Kemal Üniversitesi Adresli: Evet
Özet
Discrete Ricci curvature has been applied to biological, financial, and communication graphs, but typed management information system (MIS) transaction networks still lack MIS-specific analytical guarantees and a reproducible, operationally interpretable workflow. We combine Ollivier-Ricci optimal transport with a role-based access control representation of users, roles, services, endpoints, and databases. Closed-form results show that edges joining a hub to degree-one leaves have non-negative curvature, whereas canonical inter-hub bridges converge to curvature -1 when the idleness parameter is alpha=0.5 . We also prove the existence of an optimal coupling on finite graphs and explain why the coupling itself need not be unique. On a reproducible synthetic MIS network, the curvature ranks authentication, shared-data, and cross-module links among the leading candidate bottlenecks and correlates with edge betweenness (Spearman rho=-0.78). Across 40 randomized MIS instances, graph-instance-level edge-class differences are significant (Friedman p<10(-32)), and all five leading edges belong to predefined structural bridge classes in every run. On five public Internet backbones, curvature-betweenness correlations range from -0.53 to -0.91 . Comparisons with Forman curvature, local edge connectivity, algebraic connectivity loss, and a spectral embedding show a complementary geometric signal rather than a universal cut-edge or spectral surrogate. We additionally report the idleness parameter sensitivity, empirical runtime and process memory measurements, study limitations, and a conceptual temporal extension.